Sharif Digital Repository

Supersonic turbulent high-pressure jet flows, which are discharging in low-pressure quiescent ambient, are recognized as imperfectly expanded turbulent jet. Steady-state imperfectly expanded jet flow has been already studied analytically; however, the transient flow has not been thoroughly studied. In the present study, the transient imperfectly expanded jet flow with focus on fuel spray in combustion is investigated analytically employing two-step separation of variables method and Fourier-Bessel expansion. The results are validated using available experimental data. The effects of different parameters such as eddy viscosity and pressure ratio on the behavior of the jet are studied. Results... 

The present article aims to investigate the Graetz-Nusselt problem for blood as a non-Newtonian fluid obeying the power-law constitutive equation and flowing inside the axisymmetric tube subjected to non-uniform surface heat flux. After the flow field is determined by solving the continuity and the momentum equations, the energy equation is handled by employing the separation of variables method. The resulting Eigen functions and Eigen values are numerically calculated using MATLAB built-in solver BVP4C. The analysis is first conducted for the situation of constant heat flux and subsequently generalized to apply to the case of sinusoidal variation of wall heat flux along the tube length,... 

Recent development in technology and improvement of manufacturing tools have accelerated the use of microrobots (MRs) in numerous areas such as micro sensing and medical applications. The ability to control multiple MRs simultaneously and independently could lead to higher performance, and even make new applications possible. In this paper, we have proposed a system for simultaneous and independent control of the position of multiple MRs in a plane. The system consists of 2N permanent magnets (PMs) with a circular arrangement in the plane around the workspace and a pair of Helmholtz coil to control N MRs. PMs are rotated by servomotors, and the coil aligns the orientation of the MRs normal... 

In this article, a size-dependent generalized thermoelasticity model is established to appraise the small-scale effect on thermoelastic vibrations of Euler-Bernoulli nanobeams. Small-scale effect on the structure and heat conduction is captured by exploiting nonlocal strain gradient theory (NSGT) and nonclassical heat conduction model of Guyer and Krumhansl (GK model). NSGT enables the model to account for both nonlocal and strain gradient effects on structure, and GK formulation empowers the model to incorporate both nonlocal and lagging effect into heat conduction equation. The normalized forms of size-dependent equations of motion and heat conduction are provided by introducing some... 

This work aims to present an experimentally verified analytical solution to examine damping properties of systems including viscoelastic treatments. Although there are several methods for characterizing the behavior of three-layer damping systems, the RKU method is the most frequently used one. In this paper, this method is modified such a way that to be applied for a five-layer damping system. The achieved analytical relations are then employed to study the effects of a four-layer vibration-absorbing coating on the dynamic behavior of an aluminum sheet with free-free boundary conditions. Since the vibration-damping properties of the coating are unknowns, its loss factor and shear modulus... 

This study provides a stability analysis of flexible rotating pipes taking into account the simultaneous effects of internal and external fluid loading. Using the Euler-Bernoulli beam assumptions, governing equations for flexural vibrations of rotating pipes are obtained. The internal flow characteristics and the double gyroscopic effect are taken into account when deriving the structural equations coupled with the internal flow. External fluid loading is determined by a special linearization of the Navier-Stokes equations. Considering the circular wall of the pipe as an impermeable boundary to the flow, fluid-induced forcing functions are obtained and then applied to the structural... 

This study provides a stability analysis of flexible rotating pipes taking into account the simultaneous effects of internal and external fluid loading. Using the Euler-Bernoulli beam assumptions, governing equations for flexural vibrations of rotating pipes are obtained. The internal flow characteristics and the double gyroscopic effect are taken into account when deriving the structural equations coupled with the internal flow. External fluid loading is determined by a special linearization of the Navier-Stokes equations. Considering the circular wall of the pipe as an impermeable boundary to the flow, fluid-induced forcing functions are obtained and then applied to the structural... 

Gas condensate production using technology of multi-stage hydraulically fracturing in shale gas condensate reservoirs' horizontal wells is a new topic of unconventional resources studies. Thus, shale gas condensate as a new source of energy can be considered as an important issue for development and further studies. In this work, a semi-analytical solution of gas and oil two-phase flow is presented for pressure transient analysis (PTA) and rate transient analysis (RTA) of a shale gas condensate reservoir's production data. Fluid flow assumption here is flow in a pseudo triple-porosity porous media, which are matrix, natural fractures and adsorbed gas. Adsorbed gas is a form of gas in porous... 

The exponential growth in the semiconductor industry and hence the increase in chip complexity, has led to more power usage and power density in modern processors. On the other hand, most of today's embedded systems are battery-powered, so the power consumption is one of the most critical criteria in these systems. Dynamic Voltage and Frequency Scaling (DVFS) is known as one of the most effective energy-saving methods. In this paper, we propose the optimal DVFS profile to minimize the energy consumption of a battery-based system with uncertain task execution time under deadline constraints using the Calculus of Variations (CoV). The contribution of this work is to analytically calculate the... 

The eccentricity between the circular fiber and its coating as well as the imperfection at the fiber-coating-matrix interfaces associated with certain composites can have a remarkable effect on the movement of a dislocation. For an in-depth understanding of such phenomena, the present work provides an exact analytical solution for the interaction between an eccentrically coated circular inhomogeneity embedded in an infinite elastic medium with imperfect interfaces and a screw dislocation. The dislocation may be located inside one of the regions: the core inhomogeneity, coating, or the matrix. The corresponding boundary value problem is solved by using conformal mapping and complex potential... 

Micropumps are among useful equipment in microsystems. The magnetically actuated mercury micropump, which has been introduced for less than a decade, is an innovative kind of micropumps which uses mercury droplets motion as a pumping agent. The equations governing this micropump are complex and their numerical solution is a time-consuming process, due to electromagnetic, hydrodynamic, and unsteady effects. In the present study, for the first time, using simplifying assumptions, the performance of a Magneto Mercury Reciprocating (MMR) micropump with electromagnetic actuation is studied through electrical analogy and then, the components and operational stages of the micropump are simulated... 

Based on the first order shear deformation theory, free vibration behavior of functionally graded (FG) annular sector plates integrated with piezoelectric layers is investigated. The distribution of electric potential along the thickness direction of piezoelectric layers which is assumed to be a combination of linear and sinusoidal functions, satisfies both open and closed circuit electrical boundary conditions. Through a reformulation of governing equations and harmonic motion assumption, a novel decoupling method is suggested to transform the six second order coupled partial differential equations of motion into two eighth order and fourth order equations. A Fourier series method is then... 

In Li-ion batteries the interface between the nano-size spherical core graphite and its surrounding solid electrolyte interphase (SEI) layer, just inside SEI is susceptible to damage. Thus, accurate determination of the associated elastic fields is one of the challenges in optimizing the lifetime and capacity of Li-ion batteries. The required precision is achieved by considering the core graphite which belongs to the crystal class D6h as homogeneous spherically isotropic and SEI layer as functionally graded (FG) isotropic material. Moreover, to account for the surface/interface effects appropriately the core-shell nano-structure subjected to the diffusion-induced time-dependent nonuniform... 

This paper presents a bi-directional closed-form analytical solution, in the framework of nonlinear soft composites mechanics, for top-down hyperelastic characterization of brain white matter tissue components, based on the directional homogenized responses of the tissue in the axial and transverse directions. The white matter is considered as a transversely isotropic neo-Hookean composite made of unidirectional distribution of axonal fibers within the extracellular matrix. First, two homogenization formulations are derived for the homogenized axial and transverse shear moduli of the tissue, based on definition of the strain energy density function. Next, the rule of mixtures and... 

An exact analytical solution for one-dimensional fluid flow through rock matrix block is presented. The nonlinearity induced from flow functions makes the governing equations describing this mechanism difficult to be analytically solved. In this paper, an analytical solution to the infiltration problems considering non-linear relative permeability functions is presented for finite depth, despite its profound and fundamental importance. Elimination of the nonlinear terms in the equation, as a complex and tedious task, is done by applying several successive mathematical manipulations including: Hopf-Cole transformation to obtain a diffusive type PDE; an exponential type transformation to get a... 

Based on the nonlocal Euler–Bernoulli beam theory, a theoretical approach is developed to investigate the effects of small scale and intermolecular force on the dynamic pull-in behavior of electrostatically actuated nanoresonators. To this purpose, nanoresonators are modeled as multilayer beams with rectangular cross-sections and fixed-fixed and fixed-free end conditions which are embedded in an elastic medium containing Winkler and Pasternak elastic foundations. Also, the effects of nonlocal parameter, fringing field due to the finite width of beams, Casimir or van der Waals intermolecular forces, nonlinear term induced by mid-plane stretching and Winkler and Pasternak elastic foundations... 

Generally, in most areas, groundwater level is deep and heat sources (e.g., energy piles)are embedded in unsaturated soil media. Therefore, in order to accurately analyze the soil response close to heat sources, both heat and moisture transport in unsaturated soil domain should be considered. Thermal loading changes the moisture content in the porous media. In this study, the energy conservation and mass fluid continuity equations derived from hydrothermal analysis of a partially saturated soil medium are considered in cylindrical coordinate system. To make the analytical solution possible, partial differential equations (PDEs)are turned into ordinary differential equations (ODEs), through... 

In this paper, pull-in behavior of cantilever micro/nano-beams made of functionally graded materials (FGM) with small-scale effects under electrostatic force is investigated. Consistent couple stress theory is employed to study the influence of small-scale on pull-in behavior. According to this theory, the couple tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients. The material properties except Poisson’s ratio obey the power law distribution in the thickness direction. The approximate analytical solutions for the pull-in voltage and pull-in displacement of the microbeams are derived using the Rayleigh–Ritz method. Comparison between the results of the... 

The nonlinear governing equations of three shell theories (Donnell, Love, and Sanders) with first-order approximation and von Kármán’s geometric nonlinearity for laminated sandwich cylindrical shells with isotropic, functionally graded (FG) or isogrid lattice layers are decoupled. This uncoupling makes it possible to present a semi-analytical solution for the nonlinear bending and post-buckling behavior of short and long doubly simply supported, doubly clamped, and cantilever laminated sandwich cylindrical shells subjected to various types of thermo-mechanical loadings. The results for deflection, stress, critical axial traction, and mode shapes in FG shells are verified with those obtained... 

The nonlinear governing equations of three shell theories (Donnell, Love, and Sanders) with first-order approximation and von Kármán’s geometric nonlinearity for laminated sandwich cylindrical shells with isotropic, functionally graded (FG) or isogrid lattice layers are decoupled. This uncoupling makes it possible to present a semi-analytical solution for the nonlinear bending and post-buckling behavior of short and long doubly simply supported, doubly clamped, and cantilever laminated sandwich cylindrical shells subjected to various types of thermo-mechanical loadings. The results for deflection, stress, critical axial traction, and mode shapes in FG shells are verified with those obtained...